The fundamental concept and properties of integrals and derivatives of fractional order of a function with respect to the another function viz. \( \Psi \) -Riemann-Liouville integral and derivative have been introduced in
[1]}. Following the similar approach, Almeida [2]} introduced \(\Psi \) -Caputo fractional derivative and investigated the interesting properties of this operator and extended
few preceding study concerned with the Caputo and the Caputo–Hadamard derivative operators.
